Rain is actually very little water at any one path. A drop is falling at 10 meters per second and heavy rain is ~1 cm per hour. So to ballpark it's around 1 part in 3.5 million water on average and assuming 1mm drop size you will see ~3.6km on average before you encounter a drop.

Note this is instantaneous, human vision deals with after images which adds blur.

That's a good calculation. http://hypertextbook.com/facts/2007/EvanKaplan.shtml backs up your facts and claims that a raindrop is actually more like 6 mm, which makes the straight line view much longer.

However in the rain, on a highway, we have water falling, water splashed up from the ground, a mist formed by cars, high humidity, and a wet layer on the outside of the car. These factors reasonably could impact this device if the laser is emitting at water's absorption frequency.

I currently work on a self-driving lorry, we get around this issue by installing over a dozen lidars.